QED

QED Lagrangian

  1. Full form of the QED Lagrangian
  2. Mass of the Photon field
  3. Intermezzo 1: P and C of the photon field

    The photon field has spin J=1. In addition, the photon field has definite parity and charge conjugation. The eigenvalues are P=-1 and C=-1. In a short notation: JPC=1--.

    P and C of the photon field can be easily derived by investigating the third and fourth Maxwell equations:
    maxwell3
    and
    maxwell4
    PARITY
    Since the charge density is a scalar quantity and the Nabla operator changes its sign under a parity transformation it follows from the third Maxwell equation that the vector potential transforms as vector and hence P=-1. As a further consequence, the electric field transforms as a vector and the magnetic field as an axial-vector.

    CHARGE CONJUGATION
    Under the operation of charge conjugation the charge density and the vector current change their sign. As a consequence, the electric and magnetic field change their signs and hence also the four-potential Aμ.
  4. Intermezzo 2: Polarisation vectors of the photon field